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Initial revision

/* mpfr_log1p -- Compute log(1+x)

Copyright 2001, 2002 Free Software Foundation, Inc.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"

 /* The computation of log1p is done by

    log1p(x)=log(1+x)
 */

int
mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  int comp, inexact = 0;

  if (MPFR_IS_NAN(x)) 
    {
      MPFR_SET_NAN(y); 
      MPFR_RET_NAN;
    }

  MPFR_CLEAR_NAN(y);

  /* check for inf or -inf (result is not defined) */
  if (MPFR_IS_INF(x))
    {
      if (MPFR_SIGN(x) > 0)
        {
          MPFR_SET_INF(y);
          MPFR_SET_POS(y);
          MPFR_RET(0);
        }
      else
        {
          MPFR_SET_NAN(y);
          MPFR_RET_NAN;
        }
    }

  comp = mpfr_cmp_si(x,-1);
  /* x<-1 undefined */
  if (comp < 0) 
    {
      MPFR_SET_NAN(y);
      MPFR_RET_NAN;
    }
  /* x=0: log1p(-1)=-inf (division by zero) */
  if (comp == 0)
    {
      MPFR_SET_INF(y);
      MPFR_SET_POS(y);
      MPFR_RET_NAN;
    }

  MPFR_CLEAR_INF(y);

  if (MPFR_IS_ZERO(x))
    {
      MPFR_SET_ZERO(y);   /* log1p(+/- 0) = +/- 0 */
      MPFR_SET_SAME_SIGN(y, x);
      MPFR_RET(0);
    }

  /* General case */
  {
    /* Declaration of the intermediary variable */
    mpfr_t t;

    /* Declaration of the size variable */
    mp_prec_t Nx = MPFR_PREC(x);   /* Precision of input variable */
    mp_prec_t Ny = MPFR_PREC(y);   /* Precision of input variable */
    
    mp_prec_t Nt;   /* Precision of the intermediary variable */
    long int err;  /* Precision of error */
                
    /* compute the precision of intermediary variable */
    Nt=MAX(Nx,Ny);
    /* the optimal number of bits : see algorithms.ps */
    Nt=Nt+5+_mpfr_ceil_log2(Nt);

    /* initialise of intermediary variable */
    mpfr_init(t);             

    /* First computation of cosh */
    do {

      /* reactualisation of the precision */
      mpfr_set_prec(t, Nt);
      
      /* compute log1p */
      mpfr_add_ui (t, x, 1, GMP_RNDN);   /* 1+x */
      mpfr_log (t, t, GMP_RNDN);        /* log(1+x)*/

      /* estimation of the error */
      /*err=Nt-(_mpfr_ceil_log2(1+pow(2,1-MPFR_EXP(t))));*/
      err=Nt-(MAX(1-MPFR_EXP(t),0)+1);

      /* actualisation of the precision */
      Nt += 10;

    } while ((err<0) || !mpfr_can_round(t, err, GMP_RNDN, rnd_mode, Ny));

    inexact = mpfr_set (y, t, rnd_mode);

    mpfr_clear(t);
  }
  return inexact;
}